By Tim Kelly and Joseph CampbellTOKYO (Reuters) -Japan stands a good chance of having its first woman prime minister or its youngest leader in the modern era after a vote on Saturday to pick the head of the nation’s ruling party. They are among five candidates vying to replace Prime Minister Shigeru Ishiba, who is stepping down after a series of electoral defeats. “Koizumi and Takaichi offer two quite different approaches to that renewal,” said Tina Burrett, a political science professor at Tokyo’s Sophia University. If chosen, Koizumi would be a few months older than Hirobumi Ito when he became Japan’s first prime minister in 1885, under the nation’s prewar constitution. Takaichi, an ally of assassinated former Prime Minister Shinzo Abe, has the most expansionist economic platform of the LDP candidates.